Chow Ring of Moduli Space of Abelian Varieties - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T12:02:23Z http://mathoverflow.net/feeds/question/19477 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19477/chow-ring-of-moduli-space-of-abelian-varieties Chow Ring of Moduli Space of Abelian Varieties Charles Siegel 2010-03-26T23:50:39Z 2010-04-30T07:33:43Z <p>Is there a good reference for the structure of the Chow ring of $\mathcal{A}_g$, the moduli space of complex principally polarized abelian varieties? More generally, references for the intersection theory, enumerative geometry, and vector bundles on $\mathcal{A}_g$ would be nice.</p> http://mathoverflow.net/questions/19477/chow-ring-of-moduli-space-of-abelian-varieties/23080#23080 Answer by Jeffrey Giansiracusa for Chow Ring of Moduli Space of Abelian Varieties Jeffrey Giansiracusa 2010-04-30T07:33:43Z 2010-04-30T07:33:43Z <p>Van der Geer has written a paper computing what he calls the tautological subring of the chow ring of $\mathcal{A}_g$. He also computes the tautological ring for a smooth toroidal compactification.</p> <p>G. van der Geer, Cycles on the Moduli Space of Abelian Varieties, in "Moduli of Curves and Abelian Varieties (The Dutch Intercity Seminar on Moduli)", p. 65-89 (Carel Faber and Eduard Looijenga, editors), Aspects of Mathematics, Vieweg, Wiesbaden 1999.</p> <p>It is available on the van der Geer's website <a href="http://www.science.uva.nl/~geer/publications.html" rel="nofollow">here</a></p> <p>Regarding intersection theory, Erdenberger, Grushevsky, and Hulek have been working on this for the toroidal compactifications, mostly for small values of $g$. For example, see the following references.</p> <p>C. Erdenberger, S. Grushevsky, K. Hulek, Intersection theory of toroidal compactifications of <code>$\mathcal{A}_4$</code>. Bull. London Math. Soc. 38 (2006), no. 3, 396--400.</p> <p>C. Erdenberger, S. Grushevsky, K. Hulek, Some intersection numbers of divisors on toroidal compactifications of <code>$\mathcal{A}_g$</code>. J. Algebraic Geom. 19 (2010), no. 1, 99--132.</p> <p>S. Grushevsky, Geometry of <code>$\mathcal{A}_g$</code> and its compactifications. Algebraic geometry---Seattle 2005. Part 1, 193--234, Proc. Sympos. Pure Math., 80, Part 1, Amer. Math. Soc., Providence, RI, 2009. </p>